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Zbl 1162.70014
Ding, Yanheng; Lee, Cheng
Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system. (English)
[J] J. Differ. Equations 246, No. 7, 2829-2848 (2009). ISSN 0022-0396

Summary: This paper deals with existence and exponential decay of homoclinic orbits for the first-order Hamiltonian system $\dot z = \cal J H_z(t, z),$ where the Hamiltonian function $H(t,z)$ is nonperiodic in $t \in \Bbb R$ and superquadratic in $z \in \Bbb R^{2N}$. With certain mild conditions, we obtain the solutions via variational methods for strongly indefinite problems.

MSC 2000:: *70H05 Hamilton's equations
70K44 Homoclinic and heteroclinic trajectories
70G75 Variational methods

Keywords: critical point; mild conditions; variational methods

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